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2019 Slovenia Team Selection Test
4
4
Part of
2019 Slovenia Team Selection Test
Problems
(1)
Slovenia 2019 TST1 P4
Source: 2019 Slovenia 1st TST Problem 4
2/18/2019
Let
P
P
P
be the set of all prime numbers. Let
A
A
A
be some subset of
P
P
P
that has at least two elements. Let's say that for every positive integer
n
n
n
the following statement holds: If we take
n
n
n
different elements
p
1
,
p
2
.
.
.
p
n
∈
A
p_1,p_2...p_n \in A
p
1
,
p
2
...
p
n
∈
A
, every prime number that divides
p
1
p
2
⋯
p
n
−
1
p_1 p_2 \cdots p_n-1
p
1
p
2
⋯
p
n
−
1
is also an element of
A
A
A
. Prove, that
A
A
A
contains all prime numbers.
TST
number theory